Information on Result #2495071
Linear OOA(4124, 2097164, F4, 2, 15) (dual of [(2097164, 2), 4194204, 16]-NRT-code), using 41 times duplication based on linear OOA(4123, 2097164, F4, 2, 15) (dual of [(2097164, 2), 4194205, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4123, 4194328, F4, 15) (dual of [4194328, 4194205, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4124, 2097164, F4, 3, 15) (dual of [(2097164, 3), 6291368, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (109, 124, 2097164)-net over F4 | [i] | ||